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A note on kernel density estimators with optimal bandwidths

Author

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  • Hjort, Nils Lid
  • Walker, Stephen G.

Abstract

We show that the cumulative distribution function corresponding to a kernel density estimator with optimal bandwidth lies outside any confidence interval, around the empirical distribution function, with probability tending to 1 as the sample size increases.

Suggested Citation

  • Hjort, Nils Lid & Walker, Stephen G., 2001. "A note on kernel density estimators with optimal bandwidths," Statistics & Probability Letters, Elsevier, vol. 54(2), pages 153-159, September.
    • Handle: RePEc:eee:stapro:v:54:y:2001:i:2:p:153-159
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    Citations

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    Cited by:

    1. Alexandre Leblanc, 2012. "On estimating distribution functions using Bernstein polynomials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 919-943, October.
    2. Elisa Molanes-López & Ricardo Cao, 2008. "Plug-in bandwidth selector for the kernel relative density estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 273-300, June.
    3. Manté, Claude, 2015. "Iterated Bernstein operators for distribution function and density estimation: Balancing between the number of iterations and the polynomial degree," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 68-84.

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